Explanation Given information: W = m g = ( 80 k g ) ( 9.81 m / s 2 ) = 784.8 N M E = r H / E W = ( 0.25 m ) ( 784.8 N ) = 196.2 N . m Disk D weighs 2lb Radius of gyration is 0.9in. Disk S weighs 6lb Radius of gyration is 1.5in Consider given diagram We have to draw the triangle that connects the point POB So Explanation: Find the value of r by applying the cosines rule r 2 = 1.25 2 + 2.5 2 − 2 × 1.25 × 2.5 cos 30 0 r = 1.549 i n . And then find the angle using sine rule: sin β 1.25 = sin 30 0 r sin β 1.25 = sin 30 0 1.5491 sin β = 0.4034 β = 23.794 0 Then choose the disk S on rotating frame asreference Ω = ω s Ω ˙ = α s So consider the motion of the disk S Find the velocity of the point P V P ' = r ω s Substitute r value V P ' = [ 1.549 ω s ↘ β ] Find the acceleration of point P a P ' = − α s × r − ω S 2 r Substituting all the values we get a P ' = 1.549 α s ↘ β + 1.549 ω s 2 ↙ β And then consider the motion relative to the given frame we get: V P / S = u ↙ β a P / S = u ˙ ↙ β And then the coriolis acceleration in velocity of point P V P = 1.549 ω S ↘ β + u ↙ β − − − ( 1 ) So acceleration at point P is, a P / S = ( u ˙ ↙ β ) Formulate the coriolis component of the acceleration a C = 2 ω s u Acceleration of point p is a P = a P ' + a P / S + a c Substituting the values we get a P = 1.549 α s ↘ γ + 1.549 ω 2 s ↙ γ + u ˙ ↙ γ + 2 ω s u ↖ γ − − − ( 2 ) Choose the motion of disk D rotation to its B V P = ( r D ) ω D So we get V P = ( 1.25 ) ( 8 ) = 10 i n . / s ↙ 30 0 − − − − ( 3 ) Similarly, acceleration at point P a P = [ ( B P ) α D ↙ 60 0 ] [ ( B P ) ω D 2 ↘ 30 0 ] a P = 0 + [ ( 1.25 ) ( 8 ) 2 ↘ 30 0 ] = 80 i n . / s 2 ↘ 30 0 − − − − ( 4 ) From the equations (3) and (1) we have to resolve the components. We get, 1.549 ω s ↘ γ + u ↙ γ = 10 i n . / s ↙ 30 0 Solve the components we get 1.549 ω s ↘ γ + u ↙ γ = 10 i n . / s ↙ 30 0 1 To determine (b) Find the magnitude of the force P.

12th Edition

ISBN: 9781259977305

Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.

Publisher: Mcgraw-hill Education,

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Chapter 16, Problem 16.163RP

To determine

(a)

Find a couple of M.

To determine

(b)

Find the magnitude of the force P.

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Chapter 16, Problem 16.162RP

Chapter 16, Problem 16.164RP

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(a) Find a couple of M.

Solution Summary: The author explains how to find the value of r by applying the cosines rule.